Lefschetz properties and basic constructions on simplicial spheres

Eric Babson, Eran Nevo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The well known g-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the strong-Lefschetz property is preserved under the following constructions on homology spheres: join, connected sum, and stellar subdivisions. The last construction is a step towards proving the g-conjecture for piecewise-linear spheres.

Original languageAmerican English
Pages (from-to)111-129
Number of pages19
JournalJournal of Algebraic Combinatorics
Issue number1
StatePublished - Feb 2010
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements We deeply thank Satoshi Murai for his valuable comments on an earlier version of this paper, and Gil Kalai for helpful discussions. Further thanks go to the referees, especially one of them, whose detailed comments greatly helped to improve the presentation. Part of this work was done during the “Algebraic Combinatorics” program at the Institut Mittag-Leffler in Spring 2005. We are grateful to Anders Björner and Richard Stanley for inviting us to this program. The authors were partially supported by the European Commission’s IHRP Programme, grant HPRN-CT-2001-00272, “Algebraic Combinatorics in Europe”. Another part of this work was done during the special semester at the Institute for Advanced Studies in Jerusalem, in Spring 2007. We are grateful to IAS for the hospitality, and to Gil Kalai for organizing this semester.

Funding Information:
Research of E. Nevo was partially supported by an NSF Award DMS-0757828.


  • Face ring
  • Homology sphere
  • Strong-Lefschetz property


Dive into the research topics of 'Lefschetz properties and basic constructions on simplicial spheres'. Together they form a unique fingerprint.

Cite this